Enter the total number of trials, the number of successful trials, and the probability of success into the calculator to determine the probability of error.
Probability Of Error Formula
The following formula is used to calculate the probability of error.
PE = C(n, k) * p^k * (1-p)^{(n-k)}Variables:
- PE is the probability of error
- C(n, k) is the combination of n trials taken k at a time
- p is the probability of success on a single trial
- k is the number of successful trials
- n is the total number of trials
To calculate the probability of error, use the binomial probability formula to find the likelihood of k successes in n trials with a success probability of p on each trial. The probability of error is the complement of the probability of success.
What is Probability Of Error?
Probability of error is the likelihood that a given number of successes will not occur in a series of trials, given a certain probability of success on each trial. It is a key concept in statistics and probability theory, often used to assess the risk or uncertainty associated with a process or experiment.
How to Calculate Probability Of Error?
The following steps outline how to calculate the Probability Of Error.
- First, determine the total number of trials (n).
- Next, determine the number of successful trials (k).
- Next, determine the probability of success on a single trial (p).
- Use the binomial probability formula to calculate the probability of k successes in n trials.
- Finally, calculate the Probability Of Error (PE).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Total number of trials (n) = 30
Number of successful trials (k) = 15
Probability of success on a single trial (p) = 0.5
